Re: Roots of the term "gammatone"

["Richard F. Lyon" <DickLyon@xxxxxxx>]

And while we're on coincident roots ...

I looked a long time for uses of gammatone-like 
filters earlier and outside the hearing field. 
It seemed like such a simple structure (cascade 
of N resonators) and simple parameterization was 
sure to have been investigated before, and the 
connection to gamma distributions or gamma 
functions would likely have been noticed.

I eventually found some.  Back in the day, before 
the use of impulse response was standard, people 
used to analyze filters by their step response 
(like when Karl Kupfmuller first described the 
ideal lowpass filter by its step response, the 
"integralsinus", as opposed to its modern 
description by its sinc function  impulse 
response).

In 1945, Eaglesfield observed that the envelope 
step response of the cascade of N identical 
resonators is the "incomplete gamma function", 
which is the integral of the gamma distribution. 
So he shows the gamma distribution t^(N-1) 
exp(-t/tau) as an integrand; this envelope step 
response is implicitly multiplying a tone.  So he 
had a gammatone filter, just not the name.

Tamas, I'll send you a copy.  Also a paper by 
Tucker who investigated such filters, 1946, and 
quoted Eaglesfield on the "incomplete gamma 
function"; he also showed a fascinating 
alternative way to describe the envelope step 
response in an N-term closed form without the 
integral.

Dick

the refs:

@article{eaglesfield1945,
  author = {C. C. Eaglesfield},
  title = {Carrier Frequency Amplifiers: The Unit 
Step Response of Amplifiers with Single and 
Double Circuits},
  year = {1945},
  journal = {Wireless Engineer},
  volume = {22},
  pages = {523--532}
}

@article{tucker1946,
  author = {D. G. Tucker},
  title = {Transient Response of Tuned-Circuit Cascades},
  year = {1946},
  journal = {Wireless Engineer},
  volume = {23},
  pages = {250--258}
}


At 8:36 AM -0700 3/28/12, Richard F. Lyon wrote:
> Tamas,
>
> I recounted some of those mis-attributions in 
> http://dicklyon.com/tech/Hearing/APGF_Lyon_1996.pdf
> and concluded:
>
>   Aertsen and Johannesma [AJ80] appear to have coined the catchy name;
>   referring to the envelope, they said:
>
>     The form m(t) appears both as the integrand in the definition
>     of the Gamma function $\Gamma(g)$ and as the density function
>     of the Gamma distribution, therefore we propose to use ... the
>     term "Gamma-tone" or "$\gamma$-tone."
>
>     ... The non-hyphenated "gammatone," as an adjective modifying
>     "filter," appears to be due to Patterson et al. [P88].
>
> Dick
>
>
>
>
> At 10:05 AM +0200 3/28/12, Tamas Harczos wrote:
> > Dear List,
> >
> > I am looking for the first time use of the term "gammatone". Flanagan
> > ('65), Johannesma and de Boer ('72,'75) did not use that term. Patterson
> > et al. write in their '88 APU report "An efficient auditory filterbank
> > based on the gammatone function" that "Johannesma (1972) used this
> > function to summarize revcor data, although he did not refer to it as
> > the gammatone function, and the function was not fitted to revcor data.
> > The name appears to have been adopted by de Boer and de Jongh (1978)".
> > However, I am not able to find the term "gammatone" in the de Boer and
> > de Jongh paper "On cochlear encoding: Potentialities and limitations of
> > the reverse-correlation technique" JASA 63(1), 1978.
> >
> > Any ideas?
> > Thanks!
> > Tamas
> >
> > --
> > *~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*
> > Dipl.-Ing. Tamás Harczos
> > PhD Student
> > Institute for Media Technology
> > Faculty of Electr. Eng. and Inf. Techn.
> > Ilmenau University of Technology
> > Tel.: +49 3677 467 225
> > Fax.: +49 3677 467 4225
> > E-Mail: tamas.harczos@xxxxxxxxxxxxxxxxxx
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